BUSI 230 Review Exam 4 More Hypothesis Tests solutions complete answers

BUSI 230 Review Exam 4 More Hypothesis Tests solutions complete answers 

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SAT scores: Scores on the math SAT are normally distributed. A sample of 19 SAT scores had standard deviation =89. Someone says that the scoring system for the SAT is designed so that the population standard deviation will be at most =78. Do these data provide sufficient evidence to contradict this claim? Use the =0.01 level of significance.

 

Age discrimination: The following table presents the numbers of employees, by age group, who were promoted, or not promoted, in a sample drawn from a certain industry during the past year.

Can you conclude that the people in some age groups are more likely to be promoted than those in other age groups? Use Excel and the =0.05 level of significance.

 

Blood pressure: A blood pressure measurement consists of two numbers: the systolic pressure, which is the maximum pressure taken when the heart is contracting, and the diastolic pressure, which is the minimum pressure taken at the beginning of the heartbeat. Blood pressures were measured, in millimeters of mercury (mmHg), for a sample of  adults. The following table presents the results.

(a) Construct a scatter plot of the price of milk  versus the price of eggs .

(b) Compute the correlation coefficient between systolic and diastolic blood pressure. Round the answer to at least three decimal places.

(c) If someone's diastolic pressure is above average, would you expect that person's systolic pressure to be above or below average? Explain.

 

Great Pumpkins: When growing giant pumpkins for competitions, growers need to keep track of the weights of the pumpkins while they are growing. It is difficult to weigh a large pumpkin before it is harvested, so a method has been developed for estimating the weight. The grower measures around the pumpkin both horizontally and vertically, then adds the results. This is called the OTT (over the top) measurement and is used to predict the weight of the pumpkin. Following are the OTT measurements and actual weights of the  largest pumpkins entered into official competitions in a recent year.

Compute the least-squares regression line for predicting the weight from OTT. Round the slope and -intercept to at least four decimal places.

If two pumpkins differ in OTT by 10 inches, by how much would you predict their weights to differ? Round the answer to three decimal places.

Predict the weight of a pumpkin whose OTT is 450 inches. Round the answer to one decimal place.

 

The age of a car and the number of miles on its odometer

The association between the age of a car and the number of miles on its odometer

 

Frozen computer: A computer system administrator noticed that computers running a particular operating system seem to freeze up more often as the installation of the operating system ages. She measures the time (in minutes) before freeze-up for 6 computers one month after installation and for 6 computers seven months after installation. The results are shown. Can you conclude that the time to freeze-up is less variable in the seventh month than the first month after installation? Let  denote the variability in time to freeze-up in the first month after installation. Use the =0.05 level and the critical value method with the table.

 

A random sample of size 13 from a normal distribution has standard deviation =44. Test H=41 versus . Use the =0.01 level of significance.

The hypotheses are provided above.

Find the critical value.

Compute the test statistic. Round the answer to three decimal places as needed.

 

Babies: A sample of 25 one-year-old girls had a mean weight of 24.1 pounds with a standard deviation of 4.3 pounds. Assume that the population of weights is normally distributed. A pediatrician claims that the standard deviation of the weights of one-year-old girls is less than 6 pounds. Do the data provide convincing evidence that the pediatrician's claim is true? Use the =0.01 level of significance.

State the appropriate null and alternate hypotheses.

Find the critical value. Round the answer to three decimal places.

Compute the test statistic. Round the answer to three decimal places.

Determine whether to reject .

State a conclusion.

 

Hockey sticks: The breaking strength of hockey stick shafts made of two different graphite-kevlar composites yields the following results (in Newtons).

Can you conclude that the standard deviation of the breaking strength Composite 2 is greater? Use the =0.01 level of significance.

 

Are you smarter than your older brother? In a study of birth order and intelligence, IQ tests were given to - and -year-old men to estimate the size of the difference, if any, between the mean IQs of firstborn sons and secondborn sons. The following data for  firstborn sons and  secondborn sons are consistent with the means and standard deviations reported in the article. Assume that the samples come from normal populations.

Can you conclude that the standard deviation of IQ is greater for the firstborn than the secondborn? Let  denote the standard deviation in the IQs of firstborn sons. Use the =0.01 level.

 

False alarm: The numbers of false fire alarms were counted each month at a number of sites. The results are given in the following table.

Can you conclude that false alarms are not equally likely to occur in any month? Use the =0.01 level of significance.

 

Where do you live? The U.S. Census Bureau computed the proportion of U.S. residents who lived in each of four geographic regions in Year . Then a simple random sample was drawn of 1000 people living in the United States in Year . The following table presents the results:

Can you conclude that the proportions of people living in the various regions changed between Year  and Year ?

(a)Find the -value. Use Excel; round your answer to four decimal places.

(b)Write a conclusion.

 

Beryllium disease: Beryllium is an extremely lightweight metal that is used in many industries, such as aerospace and electronics. Long-term exposure to beryllium can cause people to become sensitized. Once an individual is sensitized, continued exposure can result in chronic beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium, workers were categorized by their duration of exposure (in years) and by their disease status (diseased, sensitized, or normal). The results were as follows:

Test the hypothesis of independence. Use the =0.05 level of significance and the P-value method with the TI-84 Plus calculator. What do you conclude?

(a) State the null and alternate hypotheses.

(b) Find the P-value. Round your answer to at least four decimal places.

(c) Determine whether to reject .

(d) State a conclusion.

 

Determine whether the association between the two variables is positive or negative.

The number of miles on a car's odometer and its resale value

The association between the number of miles on a car's odometer and its resale value is

 

Compute the correlation coefficient.

 

No smoking: The General Social Survey conducted a poll of  adults in which the subjects were asked whether they agree that the government should prohibit smoking in public places. In addition, each was asked how many people lived in his or her household. The results are summarized in the following contingency table.

Test the hypothesis of independence. Use the 0.01 level of significance and the P-value method with the TI-84 Plus calculator. What do you conclude?

(a) State the null and alternate hypotheses.

(b) Find the P-value. Round your answer to at least four decimal places.

(c) Determine whether to reject .

(d) State a conclusion.

 

The amount of money a person spends on bills per month and the amount of money the person has available to spend on entertainment

The association between the amount of money a person spends on bills per month and the amount of money the person has available to spend on entertainment is

 

The number of hours a college student spent studying in the past  hours and the number of hours the student spent sleeping in the past  hours

The association between the number of hours a college student spent studying in the past  hours and the number of hours the student spent sleeping in the past  hours is

 

Pass the ball: The NFL Scouting Combine is an event at which football scouts evaluate the abilities of some top college prospects. Following are heights in inches and weights in pounds for some of the quarterbacks at the  Combine.

(a) Construct a scatterplot of the weight  versus the height .

(b) Compute the correlation coefficient between the height and weight of the quarterbacks. Round the answer to at least three decimal places.

(c) If a quarterback is below average in height, would you expect him to be above average or below average in weight? Explain.

(d) Which of the following is the best interpretation of the correlation coefficient?

 

Compute the least-squares regression equation for the given data set. Round the slope and -intercept to at least four decimal places.

 

Price of eggs and milk: The following table presents the average price in dollars for a dozen eggs  and a gallon of milk  for certain months in a recent year. Compute the least-squares regression line for predicting the price of milk from the price of eggs.

Compute the least-squares regression line for predicting the price of milk from the price of eggs. Round the slope and -intercept to at least four decimal places.

If the price of eggs differs by $0.35 from one month to the next, by how much would you expect the price of milk to differ? Round your answer to at least two decimal places.

Predict the price of milk in a month when the price of eggs is $1.15. Round the answer to two decimal places.